JP2701795B2 - Process simulation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a process simulation method and, more particularly, to a method for predicting an internal physical quantity and shape such as an impurity profile in a semiconductor device manufacturing process.

[0002]

2. Description of the Related Art A process simulator for performing a process simulation calculates a manufacturing process of a semiconductor transistor (hereinafter, referred to as a semiconductor device) such as an oxidation process, a diffusion process, and an ion implantation process using a computer, and obtains an impurity profile of the semiconductor device. And other internal physical quantities and shapes.

For example, when oxidation or diffusion is performed on the initial shape after ion implantation, the shape change due to oxidation at each oxidation / diffusion time and the impurity diffusion in the oxidizing atmosphere are alternately released to obtain the final shape. It is possible to predict a change over time in the device shape and the impurity profile.

If the semiconductor device is optimized using the above-described process simulator so that the semiconductor device exhibits the best electrical characteristics, the cost and the period are longer than when an LSI (large-scale integrated circuit) is actually manufactured. Can be greatly reduced.

Further, since the process simulator calculates the physical quantity inside the semiconductor device, it becomes possible to analyze the behavior of impurities inside the semiconductor device.

In this process simulator, it is necessary to solve a partial differential equation such as a diffusion continuity equation representing the behavior of impurities in order to obtain a physical quantity inside the semiconductor device.
However, since the PDE cannot be solved analytically, the semiconductor device is divided into small regions, and the PDE is discretized for calculation.

[0007] For example, as an example of a method of calculating a one-dimensional profile by oxidation / diffusion, a “VLSI design / manufacturing simulation” [supervised by Michitada Morisue, CMC Corporation
Publishing, 1987], pp. 51-62 ("Chapter 3 Process Simulation 3. Process Simulator").

As an example of the case of analyzing a two-dimensional structure, there is a method of dividing a semiconductor device into small rectangular regions and discretizing a partial differential equation for calculation. This method is described in “Process Device Simulation Technology” (edited by Danyo, Sangyo Tosho, 1988), pp. 91-1.
The details are described in “3. Device simulation” described on page 22.

On the other hand, using a process simulator, LOCOS (Local Oxidation) is used.
(f) When analyzing a semiconductor device having a complicated shape such as a silicon shape or a trench structure, a method of subdividing the shape using a triangle and discretizing the shape in order to accurately represent the shape of the semiconductor device. There is. This method is described in the “Iterative Method” section.
s in Semiconductor Device
Simulation "(CS Raffert)
y, M. R. Pinto, IEEE Transact
ion on Electron Devices, V
ol. ED-32, no. 10, Oct. 1985).

That is, when a trench structure is simulated, as shown in FIGS. 8 and 9, if the shape is subdivided and divided using triangles, the shape of the semiconductor device is represented as a set of triangular elements. Therefore, the trench structure can be accurately represented.

FIG. 10 is a diagram for explaining the finite difference method using triangular elements. The solution of the partial differential equation by the finite difference method using triangular elements will be described below with reference to FIG. FIG. 10 schematically shows a part of the semiconductor device shown in FIGS.

First, the impurity concentration and the potential due to the activated impurity are defined on each lattice point (vertex of a triangle). The impurities are diffused by the concentration gradient and the potential gradient, and the flow (flux) of the impurities at that time is defined on the sides of the triangle.

According to Gauss's theorem, when a closed surface is defined, the total volume of impurities integrated in the closed surface is equal to the area integrated value of the flux perpendicular to the closed surface.

Considering the application of Gauss's theorem with respect to the above-described discretization by triangles, it is necessary to define a closed surface perpendicular to the flux. It is necessary to define a region surrounded by the vertical bisector of the side, that is, a region connecting the outer centers of the triangles. Here, the closed surface at each node (each vertex of a triangle) is generally called a control volume.

In this case, the total amount of impurities controlled by each node is obtained by multiplying the impurity concentration at that point by the volume of the control volume (in the case of two dimensions, the depth is set to 1). Is calculated and added, it becomes equal to the total dose (Dose) in the ion implantation.

Here, in order to make an appropriate control volume (closed curved surface for each node), a condition that the outer centers of adjacent triangles do not intersect with each other is essential. This is because, when the circumcenters of adjacent triangles cross each other, the cross-sectional area when the flux is integrated over the area becomes negative.

Therefore, when the above condition is not satisfied, as shown in FIG. 11, a projection of a physically impossible potential is generated. Note that a triangular mesh is partially omitted in FIG.

Further, since the control volumes intersect, the impurity concentration at that point is multiplied by the volume of the control volume to calculate the sum of all vertices of the system to be analyzed. Not equal.

In order to satisfy the condition that the circumcenters of adjacent triangles do not intersect with each other, it is necessary to guarantee the Delaunay division that there is no vertex of another triangle in the circumscribed circle of the triangle, and to perform the triangle division.

For a method of guaranteeing Delaunay division and triangulating an area, see “Tetrahedral el”.
elements and the Scharfette
r-Gummel method "(MS Moc
k, Proceeding of the NASEC
ODE IV, pp. 36-47, 1985).

For example, when a two-dimensional area is Delaunay-divided by triangular elements, according to the above-mentioned method, a material boundary point and a calculation necessary for improving the calculation accuracy are included in a group of triangles that have already been Delaunay-divided. This is a method of adding new nodes one by one.

That is, as shown in FIG. 12A, a new node is added to a group of triangles already divided by Delaunay, and a triangle having a circumscribed circle including the center node is searched. Subsequently, as shown in FIG. 12B, the searched triangle is deleted, and the outermost side of an area formed by the deleted triangle is found.

Further, as shown in FIG. 12C, a new triangle is created by connecting the outermost edge found and the new node. The triangle group newly created as described above,
It is also split by Delaunay.

[0024]

In the above-described conventional process simulator, since the shape changes when calculating the oxidation step, the discretized triangular shape also changes. Therefore, even if the above-mentioned Delaunay division is guaranteed before oxidation, the Delaunay division cannot be guaranteed because the shape of the triangle changes due to the deformation of the shape due to the oxidation. Therefore, when solving the diffusion equation calculated after oxidation, it is necessary to perform another triangulation so as to guarantee Delaunay division for the deformed shape.

[0025] Even when the triangulation that guarantees Delaunay division is performed on the deformed shape after oxidation, the shape of the triangle changes in order to recreate the triangle, and the control volume changes accordingly.

Therefore, even if the vertices of all the systems analyzed by multiplying the impurity concentration of each node by the volume of the control volume after the oxidative deformation and adding them are added, the total dose of the impurities before the oxidative deformation is preserved. Will be gone. Further, in order to improve the analysis accuracy when solving the diffusion equation, a new node may be added in some cases. However, it is necessary to define the impurity concentration of the added node.

Therefore, an object of the present invention is to solve the above-mentioned problems and to improve the impurity before oxidative deformation when performing triangulation so as to guarantee Delaunay division for the deformed shape even if the shape changes due to oxidation. The object of the present invention is to provide a process simulation method capable of storing the total dose of the process.

[0028]

A process simulation method according to the present invention is a process simulation method for performing an oxidation process and a diffusion process on a semiconductor device, wherein a triangular circumscribed circle is formed with respect to an initial shape of the semiconductor device. A step of generating a triangular mesh that guarantees Delaunay that there are no vertices of other triangles therein and has each node as a vertex; and forming the triangular mesh by connecting an outer center of each triangular mesh to the triangular mesh. A step of defining a control volume indicating a closed curved surface for each node, a step of setting an impurity concentration defined by a distance from an impurity infiltration surface of the semiconductor device for each of the nodes, and a result of the oxidation treatment are shown. Deforming the initial shape and the triangular mesh according to the result of the oxidation calculation; A step of defining a deformed control volume, and setting an impurity concentration of each node on the deformed triangular mesh based on the control volume, the deformed control volume, and an impurity concentration of each node on the triangular mesh. Generating a new triangular mesh that guarantees the Delaunay division for the deformed shape; defining a new control volume for the new triangular mesh; and forming the new control volume and the new control. Setting the impurity concentration of each node on the new triangular mesh based on the number of impurities in the region where the volume overlaps, and performing the diffusion using the impurity concentration of each node on the new triangular mesh and the new control volume. Performing a diffusion calculation for obtaining a processing result.

Another process simulation method according to the present invention is a process simulation method for performing an oxidation process and a diffusion process on a semiconductor device, wherein another triangle circumscribes a triangle with respect to the initial shape of the semiconductor device. A step of generating a triangular mesh that guarantees Delaunay division that there are no vertices of the triangle and has each node as a vertex, and for each of the nodes formed by connecting the outer center of each triangle mesh to the triangle mesh A step of defining a control volume indicating a closed curved surface, a step of setting an impurity concentration defined by a distance from an impurity infiltration surface of the semiconductor device for each of the nodes, and a result of an oxidation calculation indicating a result of the oxidation process Deforming the initial shape and the triangular mesh in accordance with A step of defining a roll volume, and a step of setting an impurity concentration of each node on the deformed triangular mesh based on the control volume, the deformed control volume, and an impurity concentration of each node on the triangular mesh. Setting a new node based on the impurity concentration of each node on the triangle mesh after the deformation, and a new triangle mesh that guarantees the Delaunay division based on the new node for the shape after the deformation. Generating, a step of defining a new control volume for the new triangular mesh, and a step of defining each node on the new triangular mesh based on the number of impurities in an area where the deformed control volume and the new control volume overlap. Setting an impurity concentration; and an impurity concentration at each node on the new triangular mesh and the new controller. And a step of performing diffusion calculation for obtaining the result of the diffusion process by using the Lumpur volume.

[0030]

In a process simulation method for oxidizing and diffusing a semiconductor device, a control volume defined for a triangle mesh, a control volume after deformation defined for a deformed triangle mesh, and a triangle mesh are defined. Based on the impurity concentration of each node above, set the impurity concentration of each node on the deformed triangle mesh based on the impurity concentration of each node, generate a new triangle mesh that guarantees Delaunay division for the deformed shape, and create a new control volume In addition to the definition, the diffusion calculation for obtaining the result of the diffusion processing is performed after setting the impurity concentration of each node on the new triangular mesh based on the number of impurities in the region where the deformed control volume and the new control volume overlap.

Thus, even when the shape changes due to oxidation, it is possible to preserve the total dose of impurities before oxidative deformation when performing triangulation so as to guarantee Delaunay division for the deformed shape. .

Further, in addition to the above processing, a step of setting a new node based on the impurity concentration of each node on the deformed triangular mesh is added, thereby suppressing a discretization error and improving analysis accuracy. It is possible to do.

[0033]

Next, the present invention will be described with reference to the drawings.

FIG. 1 is a flowchart showing a process simulation according to one embodiment of the present invention. This figure 1
A process simulation according to an embodiment of the present invention will be described with reference to FIG.

First, a process simulator (not shown)
Generates a triangular mesh that guarantees Delaunay division for the initial shape of a semiconductor device (not shown).
The generated triangle mesh is used as the triangle mesh before deformation.)
(Step S1 in FIG. 1).

The method of generating a triangular mesh that guarantees Delaunay division is described in “Tetrahedral” above.
elements and the Scharfett
er-Gummel method ", the description of the method of generating a triangular mesh that guarantees Delaunay division is omitted here.

Subsequently, the process simulator defines a control volume for the generated pre-deformation triangular mesh (hereinafter, the defined control volume is referred to as a pre-deformation control volume) (step S in FIG. 1).
2). That is, the process simulator defines, for each node (vertex shared by a plurality of triangles) of the triangle mesh before deformation, a region connecting the circumcenters of the triangles connected to each node as a control volume before deformation.

The process simulator sets the concentration of the impurity introduced by ion implantation or the like in the initial shape of the semiconductor device for each node defining the control volume before deformation (step S3 in FIG. 1).

Thereafter, the process simulator calculates the oxidation and solves the shape change due to the oxidation to predict the final shape of the semiconductor device and the time change of the impurity profile, etc., based on the result. The mesh is deformed (hereinafter, the deformed triangular mesh is referred to as a deformed triangular mesh) (step S4 in FIG. 1). In this case, the deformation of the triangular mesh is realized by changing the coordinates of each vertex of the triangle.

The process simulator deforms the control volume at each node of the deformed triangular mesh in accordance with the deformation (hereinafter, the deformed control volume is referred to as a post-deformation control volume) (FIG. 1).
Step S5).

The process simulator obtains the volume ratio of the control volume before deformation and the control volume after deformation, and calculates each node on the deformed triangular mesh based on the volume ratio and the impurity concentration of each node on the triangular mesh before deformation. Is set (step S6 in FIG. 1).

In this case, the impurity concentration at each node on the deformed triangular mesh is calculated by multiplying the impurity concentration at each node on the pre-deformed triangular mesh by the volume ratio, and the size of the deformed triangular mesh is equal to that of the pre-deformed triangular mesh. Considering that the size is larger than the size, the impurity concentration at each node on the deformed triangular mesh is made lower than the impurity concentration at each node on the pre-deformed triangular mesh.

When the impurity concentration of each node on the deformed triangular mesh is set, the process simulator generates a new triangular mesh that guarantees Delaunay division for the deformed shape of the semiconductor device. A triangular mesh is used (step S7 in FIG. 1).

The process simulator calculates the circumcenter of the new triangle mesh for each triangle and sets a control volume for each node on the new triangle mesh (hereinafter, the set control volume is referred to as a new control volume). (Step S8 in FIG. 1).

The process simulator performs figure-and-calculation of all the post-deformation control volume and the new control volume, and calculates an area where the post-deformation control volume and the new control volume overlap.

The process simulator calculates the number of impurities in each of the calculated regions, and sets the value obtained by dividing the total number of impurities in those regions by the area of the new control volume as the impurity concentration of each node on the new triangular mesh ( FIG. 1 step S9). As a result, the amount of impurities contained in the post-deformation control volume in the region where the post-deformation control volume and the new control volume overlap is transferred to the new control volume.

The process simulator uses the new triangular mesh and the new control volume set in the processing of each step described above to perform diffusion calculation to solve the impurity diffusion in the oxidizing atmosphere (step S1 in FIG. 1).
0).

FIG. 2 is a flowchart showing the processing operation of step S9 in FIG. In step S9, the amount of impurities included in the post-deformation control volume in the area where the post-deformation control volume and the new control volume overlap each other, which is calculated by the AND operation of the post-deformation control volume and the new control volume, is transferred to the new control volume. However, the method will be described below with reference to FIG.

When the process simulator receives the new control volume ICVnew (step S1 in FIG. 2)
1), the control volume ICVold after deformation corresponding to the new control volume ICVnew is extracted (step S12 in FIG. 2).

The process simulator performs figure and calculation of the new control volume ICVnew and the modified control volume ICVold, and obtains the area Sand of the area where the new control volume ICVnew and the modified control volume ICVold overlap (step S13 in FIG. 2). .

The process simulator multiplies the calculated area Sand by the impurity concentration redefined in step S6, and calculates the number of impurities Dand in a region where the new control volume ICVnew and the deformed control volume ICVold overlap (step S14 in FIG. 2). ).

The process simulator stores the calculation result (impurity number Dand) in a new control volume ICVnew.
Are sequentially added to the number of impurities Dnew (step S15 in FIG. 2).

The process simulator executes step S
The processing of 13 to S15 is a new control volume ICV
All deformed control volume ICs that overlap new
Vold is determined (step S1 in FIG. 2).
6), all control volume ICVold after deformation
If not, the next modified control volume ICVold is taken out (step S1 in FIG. 2).
9), the processes of steps S13 to S15 are repeated.

The process simulator executes the above step S
When the processes from 13 to S15 are performed on all the post-deformation control volumes ICVold, the number of impurities Dand is added to the number of impurities Dand of all the overlapping regions for the new control volume ICVnew (total number of impurities of each overlapping region). Is divided by the area of the new control volume ICVnew, and the calculation result is set as the impurity concentration at the node where the new control volume ICVnew is defined (step S17 in FIG. 2).

The process simulator executes the above step S
It is determined whether the processes of S12 and S17 and S19 have been performed for all the new control volumes ICVnew (FIG. 2).
Step S18), all new control volumes I
If it has not been performed for CVnew, the next new control volume ICVnew is taken out (step S2 in FIG. 2).
0), and repeats the processing of steps S12 to S17 and S19.

FIG. 3 is a diagram for explaining a method of setting the impurity concentration in step S3 of FIG. FIG. 3 shows the setting of the impurity concentration when an impurity is introduced into a semiconductor device by ion implantation. In the drawing, a triangular mesh is only partially drawn.

In the impurity profile by ion implantation, the impurity concentration can be defined by the distance from the material surface (semiconductor device surface) by an analytical expression.
For example, when a Gaussian distribution is used, the impurity concentration C (x)
Is expressed as C (x) = N / (2πΔR _P ) ^1/2 · exp [− (x−R _P ) ² / ΔR _P ² ] (1) Here, N is the ion implantation dose, R _P is the average projection range [peak value of the distribution curve of the impurity concentration C (x)], and x is the distance from the material surface.

Therefore, in step S3, as shown in FIG. 3, the distance x from the surface of the material to be ion-implanted to the coordinate value of each triangle vertex is calculated, and the distance x defines the impurity concentration at each triangle vertex. .

FIG. 4 is a diagram showing a process of a process simulation according to an embodiment of the present invention. FIG. 4 (a)
FIG. 4B is a diagram showing a pre-deformation triangular mesh for an initial shape that guarantees Delaunay division, and FIG. 4B is a diagram showing a pre-deformation control volume defined at a node of the pre-deformation triangular mesh.

FIG. 4 (c) is a diagram showing a deformed triangular mesh after a shape change due to oxidation, and FIG. 4 (d) is a diagram showing a deformed control volume defined at a node of the deformed triangular mesh.

FIG. 4E is a diagram showing a new triangular mesh for a deformed shape of a semiconductor device that guarantees Delaunay division, and FIG. 4F is a diagram showing a new control volume defined at a node of the new triangular mesh. It is. FIG.
(G) is a figure which shows figure and calculation of the new control volume ICVnew and the control volume ICVold after deformation | transformation.

The process of the process simulation according to one embodiment of the present invention will be described with reference to FIGS.

First, in the process simulator, a pre-deformation triangular mesh that guarantees Delaunay division with respect to the initial shape of the semiconductor device is generated based on the nodes P1 to P6 (see FIG. 4A).

That is, the process simulator sets the node P
1 to P3, a triangle mesh including nodes P2 to P4, a triangle mesh including nodes P3 to P5, a triangle mesh including nodes P3, P5, and P6, and a triangle including nodes P1, P3, and P6. Generate a mesh.

The process simulator defines a pre-deformation control volume ICVorg of the node P3 of the generated pre-deformation triangular mesh. That is, a region connecting the outer centers G1 to G5 of the triangles sharing the node P3 is defined as a pre-deformation control volume ICVorg [see FIG. 4B].

The process simulator sets the concentration of the impurity introduced by ion implantation or the like in the initial shape of the semiconductor device at the node P3 or the like defining the control volume ICVorg before deformation.

Thereafter, the process simulator performs an oxidation calculation to solve the shape change due to the oxidation to predict the final shape of the semiconductor device and the time change of the impurity profile, etc., and based on the result, the shape and the triangle of the semiconductor device. The mesh is deformed [see FIG. 4 (c)]. In this case, the coordinates of each of the nodes P1 to P6 of the pre-deformation triangular mesh are changed to become nodes Q1 to Q6.

Here, the oxidation calculation is performed by the following method. First, in the shape shown in FIG.
Laplace equation dimensions, i.e. ^{D∇ 2 C (x, y)} = 0 ...... by solving (2) determining the distribution of the oxidant in the oxide film. Where D
Is the diffusion constant of the oxidizing agent, and C (x, y) is the oxidizing agent concentration.

Next, based on the oxidizing agent concentration and the reaction constant at the interface to be oxidized, the transition of the interface to be oxidized due to volume expansion is defined as a boundary condition. Further, an equilibrium equation, that is, σ _{ij, j} = 0 (3), and a constituent relational equation, that is, σ _{i, j} = ε _kl (0) G
_ijkl (t) + ∫G _ijkl (t−γ) [∂ε _ki (γ) / ∂γ] dγ (4) is solved. Here, σ _ij is a stress component, t is time, ε _kl
Is a distortion, G _ijkl (t) is a relaxation function, and ∫ indicates integration of 0 to t, respectively.

When the equilibrium equation of equation (3) and the constitutive relational equation of equation (4) are discretized using the finite element method or the like and solved, the displacement of the vertices of each triangle is obtained. When the nodes P1 to P6 shown in FIG. 4A are moved according to the amount of the displacement, the triangle is deformed as the nodes Q1 to Q6 shown in FIG. 4C.

The above-mentioned oxidation calculation method is described in “Semiconductor Process Device Simulation Technology” (published by Realize, 1990), pp. 79-89, “Part 1 Process, Chapter 2, Process Simulation, Section 3, Two-Dimensional Oxidation. Simulation ”(Seiichi Isomae). The simulation of the above calculation is performed according to the flowchart of FIG. 4 described on page 85 of the above-mentioned document.

The process simulator defines the deformed control volume of the node Q3 of the deformed triangular mesh. That is, the outer center H of each triangle sharing the node Q3
An area connecting 1 to H5 is defined as a pre-deformation control volume ICVold [see FIG. 4D].

For example, when the triangle formed by the nodes P1 to P3 shown in FIG. 4A is transformed into the triangle formed by the nodes Q1 to Q3 shown in FIG.
The outer center G1 of the triangle composed of the nodes P1 to P3 shown in FIG.
Moves to the outer center H1 of the triangle formed by the nodes Q1 to Q3 shown in FIG.

Here, the coordinates of the node P1 are represented by (X1, Y
1), the coordinates of the node P2 are (X2, Y2), the coordinates of the node P3 are (X3, Y3), and the coordinates of the node Q1 are (X1 ′, Y
1 '), the coordinates of the node Q2 are (X2', Y2 '),
3 is (X3 ', Y3'), and if the coordinates (XG1, YG1) of the outer center G1 move linearly, the outer center H1
XH1 = X1 '+ (X2'-X1') S + (X3'-X2 ') ST (5) YH1 = Y1' + (Y2'-Y1 ') S + (Y3 '-Y2') ST (6) However, S and T in the equations (5) and (6) are as follows: S = [(XG1-X1) (Y3-Y2)-(X3-X2) (YG1-Y1)] / [(X2-X1) (Y3 -Y2)-(X3-X2) (Y2-Y1)] (7) T = [(X2-X1) (YG1-Y1)-(XG1-X1) (Y2-Y1)] / [(XG1- X1) (Y3-Y2)-(X3-X2) (YG1-Y1)] (8).

The process simulator obtains the volume ratio of the control volume before deformation ICVorg and the control volume after deformation ICVold, and based on the volume ratio and the impurity concentration of each node on the pre-deformation triangular mesh, generates the data on the deformed triangular mesh. The impurity concentration of each of the nodes Q1 to Q6 is set.

For example, when setting the impurity concentration of the node Q3, first, the impurity amount of the node P3 is calculated by multiplying the impurity concentration CP3 of the node P3 of the triangular mesh before deformation by the area of the control volume ICVorg before deformation.

This impurity amount is divided by the area of the deformed control volume ICVold to obtain the impurity concentration CQ3 at the node Q3 of the deformed triangular mesh. That is, the impurity concentration CQ3 is obtained from CQ3 = CP3.ICVorg / ICVold (9).

When the process simulator sets the impurity concentration of each of the nodes Q1 to Q6 on the deformed triangular mesh, a new triangular mesh that guarantees a new Delaunay division for the deformed shape of the semiconductor device is added to each of the nodes Q1 to Q6. This occurs at the base [see FIG. 4 (e)].

That is, the process simulator sets the node Q
Triangular mesh consisting of 1 to Q3 and nodes Q2, Q3, Q
5, a triangular mesh composed of nodes Q2, Q4 and Q5, a triangular mesh composed of nodes Q3, Q5 and Q6, and a triangular mesh composed of nodes Q1, Q3 and Q6.

The process simulator calculates the outer centers I1 to I4 for each triangle with respect to this new triangle mesh,
A new control volume ICVnew of the node Q3 on the new triangular mesh is set [see FIG. 4 (f)].

The process simulator uses the control volume ICVold after deformation and the new control volume I
Perform figure and calculation with CVnew, and transform control volume ICVold and new control volume I
The area Sand of the region where CVnew overlaps is calculated [see FIG. 4 (g)]. In addition, the area S which did not overlap this time
For S1 and S2, the area of the overlapping region with the other deformed control volume ICVold is calculated.

Control volume ICVold after deformation
And the new control volume ICVnew calculates the intersection between the transformed control volume ICVold and the new control volume ICVnew, and calculates the coordinates of the intersection and the transformed control volume ICVold.
And outer core row H1 of new control volume ICVnew
ＨH5, I1ＩI4 to determine the inside / outside of the area and calculate the AND area.

The process simulator calculates the number of impurities on the basis of the calculated areas Sand, S1 and S2, sequentially adds the numbers of impurities in these areas to calculate a total, and uses the total as a new control volume ICVnew. Is set as the impurity concentration of each node on the new triangular mesh.

The process simulator uses the new triangular mesh and the new control volume ICVnew set in the processing of each step described above to perform a diffusion calculation to solve the impurity diffusion in the oxidizing atmosphere.

In the above description, the processing is repeated for all the new control volumes ICVnew and the deformed control volumes ICVold. However, this processing method requires an O (n ² ) algorithm, which takes a very long calculation time.

Therefore, in practice, it is possible to increase the speed by using a hash table method in which an area is roughly divided into rectangles in advance, and a process such as performing AND calculation of only the control volumes included therein is performed. Become.

When the method according to the embodiment of the present invention is used for a process simulation for performing oxidation / diffusion, when the shape changes due to oxidation, the triangular division is performed again so as to guarantee Delaunay division for the deformed shape. Is performed, the total dose of impurities before oxidative deformation can be preserved.

This is a new control volume ICVne
w and the control volume ICVold after deformation are calculated and the new control volume ICVne is calculated.
The new control volume IC adjusts the dose in the area where w and the control volume ICVold after deformation overlap.
This is because it can be delivered to Vnew.

FIG. 5 is a diagram showing a comparison between a profile according to an embodiment of the present invention and an actual measurement result. FIG. 5 shows a case where boron (boron) is ion-implanted from the Si surface at an energy of 50 KeV and a dose of 5E10 ¹² cm ⁻² , and then thermally oxidized at an oxidation temperature of 90 ° C. and an oxidation time of 30 minutes. An impurity profile simulated using one embodiment of the present invention, an impurity profile simulated using a conventional technique, and a secondary ion mass spectrometry (SIMS: Secondary Ion)
Mass spectroscopy) and a comparison with an actually measured value.

The simulation results according to one embodiment of the present invention are in good agreement with the actual measurement results obtained by the secondary ion mass spectrometry in both the oxide film and the Si film. It is reduced to about 1/5 of the measurement result by the secondary ion mass spectrometry.

Here, in the actual measurement result by the secondary ion mass spectrometry, the increase in impurities near the oxide film surface is an actual measurement error due to the matrix effect caused by oxygen attachment on the surface, and the bottom of the Si side is the background. Is the effect.

When the integrated amount (dose amount) of the impurity distribution obtained by the simulation according to the embodiment of the present invention is calculated, it is 5E10 ¹² cm ^-2 , which is equal to the ion implantation dose amount of 5E10 ¹² cm ^-2 . When the integrated amount (dose amount) of the impurity distribution obtained by the simulation according to the conventional technique is calculated, it is 3E10 ¹² cm ^-2 , which does not coincide with the ion implantation dose amount of 5E10 ¹² cm ^-2 .

FIG. 6 is a flowchart showing a process simulation according to another embodiment of the present invention. A process simulation according to another embodiment of the present invention will be described with reference to FIG.

First, the process simulator generates a triangle mesh that guarantees Delaunay division for the initial shape of the semiconductor device (hereinafter, the generated triangle mesh is referred to as a pre-deformation triangle mesh) (step S21 in FIG. 6).

The method of generating a triangular mesh that guarantees Delaunay division is described in “Tetrahedral” above.
elements and the Scharfett
er-Gummel method ", the description of the method of generating a triangular mesh that guarantees Delaunay division is omitted here.

Subsequently, the process simulator defines a control volume for the generated pre-deformation triangular mesh (hereinafter, the defined control volume is referred to as a pre-deformation control volume) (step S 6 in FIG. 6).
22). That is, the process simulator defines, for each node of the pre-deformation triangular mesh, a region connecting the circumcenters of the triangles connected to each node as a pre-deformation control volume.

The process simulator sets the concentration of the impurity introduced by ion implantation or the like in the initial shape of the semiconductor device for each node defining the control volume before deformation (step S23 in FIG. 6).

Thereafter, the process simulator performs an oxidation calculation and solves the shape change due to the oxidation to predict the final shape of the semiconductor device and the time change of the impurity profile and the like, and based on the result, the shape and the triangle of the semiconductor device. The mesh is deformed (hereinafter, the deformed triangular mesh is referred to as a deformed triangular mesh) (step S24 in FIG. 6). In this case, the deformation of the triangular mesh is realized by changing the coordinates of each vertex of the triangle.

The process simulator deforms the control volume at each node of the deformed triangular mesh in accordance with the deformation (hereinafter, the deformed control volume is referred to as a post-deformation control volume) (FIG. 6).
Step S25).

The process simulator calculates the volume ratio of the control volume before deformation and the control volume after deformation, and calculates each node on the deformed triangular mesh based on the volume ratio and the impurity concentration of each node on the triangular mesh before deformation. Is set (step S2 in FIG. 6).
6).

In this case, the impurity concentration of each node on the deformed triangular mesh is calculated by multiplying the impurity concentration of each node on the pre-deformed triangular mesh by the volume ratio, and the size of the deformed triangular mesh is equal to that of the pre-deformed triangular mesh. Considering that the size is larger than the size, the impurity concentration at each node on the deformed triangular mesh is made lower than the impurity concentration at each node on the pre-deformed triangular mesh.

The process simulator adds nodes at places where the redefined impurity concentration changes abruptly, etc.
For example, the nodes are arranged such that the difference between the impurity concentrations of the adjacent nodes is within one digit (Step S27 in FIG. 6).

The process simulator sets the impurity concentration of each node on the deformed triangular mesh, and when the node is added, generates a new triangular mesh that guarantees Delaunay division for the deformed shape of the semiconductor device (hereinafter, referred to as a “triangle mesh”). ,
The generated triangle mesh is referred to as a new triangle mesh.
Step S28).

The process simulator calculates the circumcenter of each triangle on the new triangle mesh and sets a control volume for each node on the new triangle mesh (hereinafter, the set control volume is referred to as a new control volume). (Step S29 in FIG. 6).

The process simulator performs figure-and-calculation of all the post-deformation control volumes and the new control volume, and calculates an area where the post-deformation control volume and the new control volume overlap.

The process simulator calculates the number of impurities in each of the calculated regions, and sets a value obtained by dividing the total number of impurities in those regions by the area of the new control volume as the impurity concentration of each node on the new triangular mesh ( FIG. 6 step S30). As a result, the amount of impurities contained in the post-deformation control volume in the region where the post-deformation control volume and the new control volume overlap is transferred to the new control volume.

The process simulator uses the new triangular mesh and the new control volume set in the processing of each step described above to perform diffusion calculation to solve the impurity diffusion in the oxidizing atmosphere (step S3 in FIG. 6).
1).

FIG. 7 is a diagram showing a process of a process simulation according to another embodiment of the present invention. FIG.
(A) is a figure which shows the control volume after deformation | transformation defined at the node of the deformation | transformation triangular mesh.

FIG. 7B is a diagram showing a new triangular mesh for a deformed shape of a semiconductor device that guarantees Delaunay division, and FIG. 7C is a diagram showing a new control volume defined at a node of the new triangular mesh. It is. FIG.
(D) is a diagram showing the figure and calculation of the new control volume ICVnew and the modified control volume ICVold.

A process of a process simulation according to another embodiment of the present invention will be described with reference to FIGS. Note that the processing up to the point before defining the control volume after the deformation at the node of the deformed triangular mesh is the same as that of the embodiment of the present invention, so that the description is omitted.

The process simulator defines the deformed control volume of the node Q3 of the deformed triangular mesh. That is, the outer center H of each triangle sharing the node Q3
An area connecting 1 to H5 is defined as a pre-deformation control volume ICVold (see FIG. 7A).

The process simulator obtains the volume ratio of the control volume before deformation ICVorg and the control volume after deformation ICVold, and calculates each node on the deformed triangular mesh based on the volume ratio and the impurity concentration of each node on the triangular mesh before deformation. The impurity concentrations of Q1 to Q6 are set.

When the process simulator sets the impurity concentration of each of the nodes Q1 to Q6 on the deformed triangular mesh, a new triangular mesh that guarantees a new Delaunay division for the deformed shape of the semiconductor device is added to each of the nodes Q1 to Q7. This occurs at the base [see FIG. 7 (b)].

Here, as a result of setting the impurity concentration of each of the nodes Q1 to Q6, the node Q7 is set so that the difference of the impurity concentration among all the nodes Q1 to Q6 is within one digit.
1 is a node added between node 1 and node Q2.

That is, assuming that the difference in impurity concentration between the nodes Q1 and Q2 is two digits or more, the process simulator sets the node Q7 at the midpoint between the nodes Q1 and Q2.
Add. After adding the node Q7, the process simulator adds a new triangular mesh to each node Q in step S28.
It is generated based on 1 to Q7.

That is, the process simulator sets the node Q
1, Q3, Q7, and nodes Q2, Q
3 and Q5, and nodes Q2, Q3 and Q
7, a triangular mesh composed of nodes Q2, Q4 and Q5, a triangular mesh composed of nodes Q3, Q5 and Q6, and a triangular mesh composed of nodes Q1, Q3 and Q6.

The process simulator calculates the outer centers I1 to I6 for each triangle with respect to this new triangle mesh,
A new control volume ICVnew of the node Q3 on the new triangular mesh is set (see FIG. 7C).

In the process simulator, the control volume ICVold after deformation and the new control volume I
Perform figure and calculation with CVnew, and transform control volume ICVold and new control volume I
Areas Sand, S1, S2 of areas where CVnew overlaps
Are calculated respectively [see FIG. 7 (d)].

Control volume ICVold after deformation
And the new control volume ICVnew calculates the intersection between the transformed control volume ICVold and the new control volume ICVnew, and calculates the coordinates of the intersection and the transformed control volume ICVold.
And the new control volume ICVnew determines the inside and outside of the area from the outer core rows H1 to H5 and J1 to J5 to calculate the AND area.

The process simulator calculates the number of impurities in each of the calculated regions, and sets the value obtained by dividing the total number of impurities in those regions by the area of the new control volume ICVnew as the impurity concentration at each node on the new triangular mesh. .

The process simulator uses the new triangular mesh and the new control volume ICVnew set in the processing of each of the above-described steps to perform a diffusion calculation in order to solve the impurity diffusion in the oxidizing atmosphere.

The analysis accuracy at the time of solving the diffusion equation depends on the discrete error when the shape is discrete by triangles. In another embodiment of the present invention, when adding the node Q7, the difference between the impurity concentrations of the adjacent nodes is set to be equal to or less than a certain value (one digit or less). It is possible to improve.

As described above, in the process simulation method for performing the oxidation process and the diffusion process on the semiconductor device, the control volume defined for the triangular mesh and the post-deformation control defined for the deformed triangular mesh are used. Based on the volume and the impurity concentration of each node on the triangle mesh, the impurity concentration of each node on the deformed triangle mesh is set, and a new triangle mesh that guarantees Delaunay division for the deformed shape is generated. Diffusion control to define the new control volume and set the impurity concentration at each node on the new triangular mesh based on the number of impurities in the area where the deformed control volume and the new control volume overlap, and then calculate the diffusion result By doing so, even if the shape changes due to oxidation, It is possible to save the total dose of the impurity before oxidation deformation when triangulation to ensure Delaunay division with respect to shape.

Further, in addition to the above-described processing, a step of setting a new node based on the impurity concentration of each node on the deformed triangular mesh is added. When triangulation is performed so as to guarantee Delaunay division with respect to the set shape, the total dose of impurities before oxidative deformation can be preserved, discretization errors can be suppressed, and analysis accuracy can be improved.

[0125]

As described above, according to the process simulation method of the present invention, in a process simulation method for performing an oxidation process and a diffusion process on a semiconductor device, a control volume, a control volume after deformation, and each A step of setting the impurity concentration of each node on the deformed triangle mesh based on the impurity concentration of the node, a step of generating a new triangle mesh that guarantees Delaunay division for the deformed shape, and a step of generating a new triangle mesh A step of defining a new control volume, and a step of setting the impurity concentration of each node on the new triangular mesh based on the number of impurities in a region where the deformed control volume and the new control volume overlap,
A step of performing a diffusion calculation to obtain a result of the diffusion process using the impurity concentration of each node on the new triangular mesh and the new control volume, even when the shape changes due to oxidation, When triangulation is performed so as to guarantee Delaunay division, the total dose of impurities before oxidative deformation can be saved.

According to another process simulation method of the present invention, in addition to the above steps, a step of setting a new node based on the impurity concentration of each node on the deformed triangular mesh is added. Thereby, even when the shape changes due to oxidation, the total dose of impurities before oxidative deformation can be preserved when performing triangulation so as to guarantee Delaunay division for the deformed shape,
There is an effect that the discretization error can be suppressed and the analysis accuracy can be improved.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a process simulation according to an embodiment of the present invention.

FIG. 2 is a flowchart showing a processing operation of step S9 in FIG. 1;

FIG. 3 is a diagram for explaining a method of setting an impurity concentration in step S3 of FIG. 1;

4A is a diagram showing a pre-deformation triangular mesh for an initial shape that guarantees Delaunay division in one embodiment of the present invention, and FIG. 4B is defined as a node of the pre-deformation triangular mesh in one embodiment of the present invention; FIG. 4C is a diagram showing a modified control volume before deformation, FIG. 4C is a diagram showing a deformed triangular mesh after shape change due to oxidation in one embodiment of the present invention, and FIG. 5D is a node of the deformed triangular mesh in one embodiment of the present invention. Figure showing the control volume after deformation defined in
(E) is a diagram showing a new triangular mesh for a deformed shape of a semiconductor device that guarantees Delaunay division in one embodiment of the present invention, and (f) is a new triangular mesh defined as a node of the new triangular mesh in one embodiment of the present invention. FIG. 7G is a diagram showing a control volume, and FIG. 7G is a diagram showing graphic and calculation of a new control volume ICVnew and a modified control volume ICVold in one embodiment of the present invention.

FIG. 5 is a diagram showing a comparison between a profile and an actual measurement result according to an embodiment of the present invention.

FIG. 6 is a flowchart illustrating a process simulation according to another embodiment of the present invention.

FIG. 7A is a diagram showing a control volume after deformation defined at a node of a deformed triangular mesh according to another embodiment of the present invention, and FIG. 7B is a diagram showing guaranteed Delaunay division according to another embodiment of the present invention. FIG. 3C is a diagram showing a new triangular mesh for a deformed shape of a semiconductor device, FIG. 3C is a diagram showing a new control volume defined at a node of the new triangular mesh in another embodiment of the present invention, and FIG. FIG. 11 is a diagram showing a graphic AND calculation of a new control volume ICVnew and a modified control volume ICVold in the embodiment.

FIG. 8 is a sectional view showing a conventional semiconductor device.

9 is a diagram showing an example in which a triangular mesh is applied to the semiconductor device shown in FIG. 8;

FIG. 10 is a diagram showing a current in a triangular mesh and an integration region thereof.

FIG. 11 is a diagram showing an incorrect simulation result in the conventional example.

12A is a diagram illustrating a search for a triangle having a circumscribed circle including a new node, FIG. 12B is a diagram illustrating deletion of the triangle searched in FIG. 12A, and FIG. 12C is a diagram illustrating creation of a new triangle; FIG.

[Explanation of symbols]

G1 to G5 Outer centers of the pre-deformed triangular mesh H1 to H5 Outer centers of the deformed triangular mesh I1 to I5, J1 to J6 Outer centers of the new triangular mesh P1 to P6 Nodes of the pre-deformed triangular mesh Q1 to Q6 Nodes of the deformed triangular mesh ICVorg Control volume of the pre-deformed triangle mesh ICVold Control volume of the deformed triangle mesh ICVnew Control volume of the new triangle mesh Sand Area of the area where the control volume of the deformed triangle mesh and the control volume of the new triangle mesh overlap.

──────────────────────────────────────────────────続 き Continued on the front page (51) Int.Cl. ⁶ Identification code Agency reference number FI Technical display location G06F 15/60 636B

Claims (4)

(57) [Claims] 1. A process simulation method for performing an oxidation process and a diffusion process on a semiconductor device, comprising: a Delaunay division in which a vertex of another triangle does not exist in a circumcircle of the triangle with respect to an initial shape of the semiconductor device. And generating a triangular mesh having each node as a vertex, and defining a control volume indicating a closed curved surface for each node formed by connecting an outer center of each triangle mesh to the triangle mesh. Setting an impurity concentration defined by a distance from an impurity penetrating surface of the semiconductor device for each of the nodes; and setting the initial shape and the initial shape according to a result of an oxidation calculation indicating a result of the oxidation process. Deforming the triangular mesh; defining a deformed control volume for the deformed triangular mesh; Setting the impurity concentration of each node on the deformed triangular mesh based on the trawl volume, the deformed control volume, and the impurity concentration of each node on the triangular mesh; A step of generating a new triangular mesh that guarantees Delaunay division; a step of defining a new control volume for the new triangular mesh; and, based on the number of impurities in an area where the deformed control volume and the new control volume overlap. Setting an impurity concentration of each node on the new triangular mesh; and performing a diffusion calculation to obtain a result of the diffusion process using the impurity concentration of each node on the new triangular mesh and the new control volume. A process simulation method comprising: 2. The step of setting an impurity concentration at each node on the new triangular mesh includes: calculating an area of each of the deformed control volumes overlapping with the new control volume; and calculating an impurity count of each of the overlapping areas. And calculating a value obtained by dividing the total number of impurities in the overlapping region by the area of the new control volume as the impurity concentration of each node on the new triangular mesh. Item 3. The process simulation method according to Item 1. 3. A process simulation method for performing an oxidation process and a diffusion process on a semiconductor device, wherein the Delaunay division is such that a vertex of another triangle does not exist in a circumcircle of the triangle with respect to an initial shape of the semiconductor device. And generating a triangular mesh having each node as a vertex, and defining a control volume indicating a closed curved surface for each node formed by connecting an outer center of each triangle mesh to the triangle mesh. Setting an impurity concentration defined by a distance from an impurity penetrating surface of the semiconductor device for each of the nodes; and setting the initial shape and the initial shape according to a result of an oxidation calculation indicating a result of the oxidation process. Deforming the triangular mesh; defining a deformed control volume for the deformed triangular mesh; Setting the impurity concentration of each node on the deformed triangle mesh based on the trawl volume, the deformed control volume, and the impurity concentration of each node on the triangle mesh; Setting a new node based on the impurity concentration of each node; generating a new triangular mesh that guarantees the Delaunay division based on the new node for the deformed shape; and Defining a new control volume for; and setting an impurity concentration of each node on the new triangular mesh based on the number of impurities in an area where the deformed control volume and the new control volume overlap. Using the impurity concentration of each node on the new triangular mesh and the new control volume, the diffusion process is performed. Process simulation method characterized by a step of performing a diffusion calculation for obtaining the results. 4. The step of setting an impurity concentration at each node on the new triangular mesh includes: calculating a region with each of the deformed control volumes overlapping with the new control volume; and calculating an impurity number of each of the overlapping regions. And calculating a value obtained by dividing the total number of impurities in the overlapping region by the area of the new control volume as the impurity concentration of each node on the new triangular mesh. Item 3. The process simulation method according to Item 3.